2016/05/16 by Stephen Smith, Smith, Stephen, Ramon Grima +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1605.05557
arxiv created 2016/05/16 · openalex publication_date 2016/05/16 · arxiv updated 2016/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve exactly and analytically, aside from some trivial systems. We here give the first exact analytical solution to a non-trivial Brownian dynamics system: the reaction A+B\xrightleftharpoons[]C in equilibrium in one-dimensional periodic space. The solution is a function of the particles' diffusion coefficients, radii, length of space and unbinding distance.